Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $D^n$ be the closed unit disk in $\mathbb{R}^n$. I'm looking for a homeomorphism of $D^n$ to itself which is the identity on the boundary, and takes the origin to a given point $z$ in its interior. I can visualize such a function as "shifting around the mass" within $D^n$, but I can't seem to write one down.

share|improve this question
add comment

1 Answer

up vote 4 down vote accepted

Map the rays starting at $z$ to the rays starting at the origin. Each ray is identified by its point on the boundary.

share|improve this answer
1  
for a unit vector $x$ and $t\in[0,1]$ you can use $tx\mapsto z+t(x-z$) –  yoyo Mar 1 '11 at 15:45
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.